ON
THE EVOLUTION OF STRUCTURE, IN TURBULENCE PHENOMENA
Luís
G.D. de Calvão Borges
Abstract. We study the evolution of coherent structures in arbitrary turbulence phenomena, developing some tools, from non-archimedean analysis and algebraic geometry, in order to model its display. We match the scale-dependent, topological structure of the physical fields subsumed by these coherent structures with the phase portraits of some convenient, non-archimedean dynamical systems whose set we endow with a law of action. Finally, we obtain the proposition of an extremum principle for this action to define a geodesic path, as the modelized coherent structures evolve, and we delineate the conception of two experiments, derived from the fields of fluid and plasma turbulence, to test its efectiveness.
Key words and phrases: turbulence; coherent structures; Stone duality; polyadic algebras; analytic extension through a T-filter; modular elliptic curves and modular forms; rigid analytic structure.
2000 M.S.C.: Primary 76F99; Secondary 03G99, 11F66, 14H52, 32D15, 32C99, 54H99.
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On the Evolution of Structure in Turbulence Phenomena.
Index:
2. Uniqueness under the proper constraints.
3. Existence.
4. Factorization (main result).
5. Match between L-functions.
6. Match with experimental data.
7. Final considerations.
8. References.
9. Glossary.